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United States Patent |
6,208,776
|
Prohaska
,   et al.
|
March 27, 2001
|
Birefringent fiber grating sensor and detection system
Abstract
A sensor system comprises a broadband light source, a birefringent sensor,
a detection circuit, and a signal processing unit. The preferred detection
circuit further includes a variable frequency oscillator, a modulator, and
a photodetector. The modulator modulates the output of the birefringent
sensor with a modulation signal from the variable frequency oscillator.
The modulation produces an interference signal having a variable
interference frequency. By determining the frequency of the modulation
signal from the variable frequency oscillator that minimizes the
interference frequency, the detection system is able to determine the
difference in frequency between first and second spectral components of
the output of birefringent sensor. The detector may be constructed using
entirely solid state optics/electronics. The preferred fiber grating
sensor comprises a birefringent optical fiber having a cladding and a
core. The cladding has first and second side holes formed therein that
extend substantially parallel to the core, and that are substantially
coextensively located with respect to each other along the length of the
optical fiber. The first and second side holes are preferable positioned
such that, in transverse cross section of the optical fiber, a first
radial line that extends from the core to the first side hole is
substantially perpendicular to a second radial line that extends from the
core to the second side hole.
Inventors:
|
Prohaska; John D. (Torrance, CA);
Kempen; Lothar U. (Redondo Beach, CA);
Lieberman; Robert A. (Torrance, CA)
|
Assignee:
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Physical Optics Corporation (Torrance, CA)
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Appl. No.:
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057067 |
Filed:
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April 8, 1998 |
Current U.S. Class: |
385/13; 385/37; 385/125 |
Intern'l Class: |
G02B 6/1/6 |
Field of Search: |
385/12,13,123,125,37
|
References Cited
U.S. Patent Documents
4354736 | Oct., 1982 | Maklad et al. | 350/96.
|
4478489 | Oct., 1984 | Blankenship et al. | 350/96.
|
4480897 | Nov., 1984 | Okamoto et al. | 350/96.
|
4681399 | Jul., 1987 | Hicks, Jr. | 350/96.
|
4882716 | Nov., 1989 | Lefevre et al. | 367/149.
|
5009107 | Apr., 1991 | Grasdepot | 73/705.
|
5054922 | Oct., 1991 | Kersey.
| |
5064270 | Nov., 1991 | Turpin et al. | 350/96.
|
5309540 | May., 1994 | Turpin et al. | 385/123.
|
5361130 | Nov., 1994 | Kersey et al.
| |
5515459 | May., 1996 | Farhadiroushan.
| |
5615295 | Mar., 1997 | Yoshida et al. | 385/123.
|
5627921 | May., 1997 | Lidgard et al. | 385/12.
|
5680489 | Oct., 1997 | Kersey.
| |
5689578 | Nov., 1997 | Yamauchi et al. | 385/123.
|
5828059 | Oct., 1998 | Udd | 250/227.
|
5841131 | Nov., 1998 | Schroeder et al. | 250/227.
|
Foreign Patent Documents |
62-257037 | Nov., 1987 | JP.
| |
Other References
Hariharan, P. "Appendix I: Heterodyne Interferometry" Basics of
Interferometry, Acadermic Press, 1992. [no month].
Croucher, J.A., L. Gomez-Rojas, S. Kanellopoulos, V.A Handerek. "High
Sensitivity Pressure Measurements Using Side-Hole Fibre" 12th
International Conference on Optical Fiber Sensors, 1997 Technical Digest
Series, Vol. 16 Oct.28-31, 1997, Williamsburg, Virginia.
|
Primary Examiner: Lee; John D.
Assistant Examiner: Connelly-Cushwa; Michelle R.
Attorney, Agent or Firm: Nilles & Nilles, S.C.
Claims
We claim:
1. A fiber grating sensor comprising a birefringent optical fiber having a
cladding and a core, the cladding having first and second side holes
formed therein that extend substantially parallel to the core, the first
and second side holes being substantially coextensively located with
respect to each other along the length of the optical fiber, and the first
and second side holes being positioned such that, in transverse cross
section of the optical fiber, a first radial line that extends from the
core to the first side hole is sufficiently non-parallel and
non-coincident with a second radial line that extends from the core to the
second side hole to measure differential pressure exerted on the sensor
between pressure exerted on the first side hole and pressure exerted on
the second side hole.
2. A sensor as defined in claim 1, wherein the cladding has an access hole
formed therein that extends radially from one of the first and second side
holes to an exterior surface of the optical fiber.
3. A sensor as defined in claim 1,
wherein the cladding further has third and fourth side holes formed therein
that extend substantially parallel to the core and that are substantially
coextensively located with respect to each other and with respect to the
first and second side holes along the length of the optical fiber, and
wherein the third side hole is substantially colinearly located with
respect to the first side hole and the core and the fourth side hole is
substantially colinearly located with respect to the second side hole and
the core.
4. A sensor as defined in claim 1, wherein the core has a fiber grating
recorded therein, the fiber grating being generally transmissive but being
reflective in first and second positive narrow-banded spectral regions,
the first and second spectral regions being respectively centered about
first and second wavelengths, the spectral separation between the first
and second wavelengths varying in accordance with a parameter sensed by
the sensor.
5. A sensor as defined in claim 4, wherein the first side hole contains a
magneto-strictive material and wherein the parameter sensed by the sensor
is the intensity of a magnetic field.
6. A sensor as defined in claim 4, wherein the first side hole contains a
electro-strictive material and wherein the parameter sensed by the sensor
is the intensity of an electric field.
7. A sensor as defined in claim 4, wherein the first side hole contains a
material with a known thermal expansion coefficient, and wherein the
parameter sensed by the sensor is the temperature of the material.
8. A sensor as defined in claim 4, wherein the first side hole contains a
material that deforms under the influence of a specific chemical
substance, and wherein the parameter sensed by the sensor is the
concentration of the specific chemical substance.
9. A sensor as defined in claim 4,
wherein the cladding has an access hole formed therein that extends
radially from the first side hole to an exterior surface of the optical
fiber;
wherein the access hole permits a fluid to flow into the first side hole
from a location external to the optical fiber; and
wherein the parameter sensed by the sensor is the pressure of the fluid.
10. A sensor as defined in claim 4,
wherein the first side hole contains a first parameter sensing material and
the second side hole contains a second temperature compensating material;
wherein the first parameter sensing material applies a first strain to the
fiber grating, a portion of the first strain being caused by the parameter
sensed by the birefringent sensor and a portion of the first strain being
caused by thermal expansion properties of the first parameter sensing
material;
wherein the second temperature compensating material applies a second
strain to the fiber grating, the second strain being caused by thermal
expansion properties of the second temperature compensating material; and
wherein the second strain substantially offsets the portion of the first
strain caused by thermal expansion properties of the first parameter
sensing material.
11. A sensor as defined in claim 1, wherein the first radial line and the
second radial line are substantially perpendicular.
12. A fiber grating sensor comprising a birefringent optical fiber having a
cladding and a core,
(A) the cladding having first, second, third and fourth side holes formed
therein that extend substantially parallel to the core,
(1) the first, second, third and fourth side holes being substantially
coextensively located with respect to each other along the length of the
optical fiber, and
(2) the first, second, third and fourth side holes being positioned such
that, in transverse cross section of the optical fiber, a first line that
extends from the first side hole through the core to the third side hole
is sufficiently non-parallel and non-coincident with a second line that
extends from the second side hole through the core to the fourth side hole
to measure differential pressure exerted on the sensor between pressure
exerted on the first side hole and pressure exerted on the second side
hole;
(B) the cladding having first, second, third and fourth access holes formed
therein,
(1) the first and second access holes extending from an exterior surface of
the optical fiber to the first side hole, and
(2) the third and fourth access holes extending from an exterior surface of
the optical fiber to the third side hole; and
(C) the core having a fiber grating recorded therein, the fiber grating
being generally transmissive but being reflective in first and second
positive narrow-banded spectral regions, the first and second spectral
regions being respectively centered about first and second wavelengths,
the spectral separation between the first and second wavelengths varying
in accordance with a parameter sensed by the birefringent sensor.
13. A sensor as defined in claim 12,
wherein the first and second access holes cooperate with the first side
hole to provide a first fluid channel through the cladding through which a
fluid having a first fluid pressure may flow;
wherein the third and fourth access holes cooperate with the third side
hole to provide a second fluid channel through the cladding through which
a fluid having a second fluid pressure may flow; and
wherein the spectral separation between the first and second wavelengths
varies in accordance with the first and second fluid pressures.
14. A sensor as defined in claim 13,
wherein the cladding further has fifth, sixth, seventh and eighth access
holes formed therein, the fifth and sixth access holes extending from an
exterior surface of the optical fiber to the second side hole, and the
seventh and eighth access holes extending from an exterior surface of the
optical fiber to the fourth side hole;
wherein the fifth and sixth access holes cooperate with the second side
hole to provide a third fluid channel through the cladding through which a
fluid having a third fluid pressure may flow;
wherein the seventh and eighth access holes cooperate with the fourth side
hole to provide a fourth fluid channel through the cladding through which
a fluid having a fourth fluid pressure may flow; and
wherein the spectral separation between the first and second wavelengths
also varies in accordance with the third and fourth fluid pressures.
15. A sensor as defined in claim 14, wherein the first and second fluid
channels are coupled to a first common supply of fluid, wherein the third
and fourth fluid channels are coupled to a second common supply of fluid,
and wherein the system measures differential fluid pressure between the
first common supply of fluid and the second common supply of fluid.
16. A sensor as defined in claim 12, wherein the first line and the second
line are substantially perpendicular.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to birefringent fiber grating sensor systems
and methods. In particular, the present invention relates to a
birefringent fiber grating sensor system having a fiber grating sensor
formed of an optical fiber with a plurality of side holes. In another
embodiment, the present invention relates to a detection circuit for a
birefringent fiber grating sensor system.
2. Description of the Invention
Various types of fiber optic sensor systems are known. In such systems, a
transducer mechanism is used that affects the properties of light in an
optical fiber in a manner that can be detected and that is indicative of a
sensed parameter.
One example of such a transducer mechanism is a fiber grating sensor formed
of a Bragg fiber grating recorded in a birefringent fiber. A Bragg grating
comprises a periodic or semi-periodic refractive index structure recorded
of an optical fiber. In the refractive index structure, the effective
index of refraction is varied at a given spatial period (defined by a
grating constant .LAMBDA.) along the length of the optical fiber. At a
particular wavelength of the light, the period of the refractive index
structure corresponds to the wavelength of the light guided in the optical
fiber. Consequently, a resonance condition which is thereby created causes
the light to reflect backwards. This resonance condition is known as the
Bragg condition, and is stated mathematically as follows:
.lambda..sub.B =2n.sub.eff.LAMBDA. (1)
where .lambda..sub.B is the wavelength of light that is reflected
backwards, n.sub.eff is the effective index of refraction of the
propagating mode, and .LAMBDA. is the grating constant or period of the
Bragg grating. In practice, real world constraints prevent the Bragg
grating from being reflective only at the infinitesimally narrow spectral
region defined by the discrete wavelength .lambda..sub.B. Instead, the
Bragg grating is reflective in a narrow-banded spectral region that is
centered about the wavelength .lambda..sub.B. Mathematically, however, the
narrow-banded spectral region can be modeled as occurring at the discrete
wavelength .lambda..sub.B. This simplification works quite well, and is
utilized throughout the discussion contained herein.
In a birefringent fiber, light of one polarization experiences a different
effective index of refraction than light of an orthogonal polarization.
Thus, with reference to Eq. (1), it is seen that a Bragg grating recorded
in a birefringent fiber reflects light at two different wavelengths.
This arrangement has been used to implement a pressure sensor. When
pressure is applied to the pressure sensor, there is a change in the
birefringence of the optical fiber and therefore a change in the spectral
separation between the two wavelengths that are reflected. The change in
separation of the two wavelengths is proportional to the amount of
pressure applied. Thus, by monitoring the separation between the two
wavelengths that are reflected, an indication of the pressure applied to
the pressure sensor is obtained.
Fiber optic sensors enjoy popularity because they have several advantages
over other types of sensors. First, because fiber optic sensors are
non-conductive, they are particularly safe in applications where
spark-induced fires or explosions are a concern. Additionally, for the
same reason, fiber optic sensors are generally immune to lightning strikes
and other sources of electromagnetic pulses or interference. Finally,
fiber optic sensors, and in particular fiber grating sensors, can be
fabricated in the optical fiber itself. Such fiber optic sensors are
particularly easy to combine in wavelength-division multiplexed and/or
time-division multiplexed fashion by disposing the sensors at various
locations along an optical fiber.
However, several difficulties have been encountered in conjunction with
fiber optic sensors systems, and more specifically in conjunction with
birefringent fiber grating sensor systems. First, existing birefringent
sensor systems do not exhibit satisfactory sensitivity. The change in
birefringence of a birefringent sensor is in part caused by the
geometrical asymmetry that occurs when the optical fiber deforms under
strain. However, being made of glass, optical fibers are relatively
difficult to deform and sensitivity is thereby limited. Moreover,
traditional birefringent sensor systems have used detection techniques
with limited sensitivity. Thus, what is needed is a fiber grating sensor
arrangement that is more sensitive to sensed parameters such as pressure.
Second, existing birefringent sensor systems utilize sensor arrangements
that are of limited flexibility. For example, in the context of pressure
sensors, many existing fiber grating sensor arrangements are unable to
measure differential pressure. Additionally, many existing fiber grating
sensor arrangements do not provide temperature compensation. Thus, what is
also needed is a fiber grating sensor arrangement that exhibits improved
flexibility.
Finally, existing birefringent sensor systems utilize bulky detection
systems that are implemented with free space (non-solid state) optics. The
detection system is used to determine the spectral separation of the two
reflections. Existing detection systems employ high resolution
spectrometer techniques, such as performing a Fourier analysis on the
coherence function of the reflected light to determine the spectral
characteristics of the reflected light. However, in order to obtain high
resolution coherence measurements, existing detection systems utilize an
interferometer implemented with free space (non-solid state) optics. Such
interferometers tend to be quite bulky and must operate in a low vibration
(preferably, vibration-free) environment. Thus, what is needed is a
detection system that can be implemented entirely in solid state
optics/electronics but that exhibits the same sensitivity as more bulky,
free space optics-based detection systems.
BRIEF SUMMARY OF THE INVENTION
The present invention overcomes these drawbacks of the prior art.
Specifically, in accordance with one aspect of the invention, the present
invention provides a fiber grating sensor comprising a birefringent
optical fiber having a cladding and a core. The cladding has first and
second side holes formed therein that extend substantially parallel to the
core, and that are substantially coextensively located with respect to
each other along the length of the optical fiber. The first and second
side holes are positioned such that, in transverse cross section of the
optical fiber, a first radial line that extends from the core to the first
side hole is non-parallel and non-coincident with a second radial line
that extends from the core to the second side hole.
Preferably, additional side holes are formed in the cladding. Additionally,
the cladding preferably is provided with one or more access holes that
extend radially from one of the side holes to an exterior surface of the
optical fiber. For example, in one preferred embodiment, two side holes
are filled with fluid and two orthogonal side holes are filled with air.
Four access holes are provided for the two side holes filled with fluid.
The access holes permit fluid to flow through the sensor so that the
sensor may be used to determine the pressure of the fluid. Advantageously,
the provision of two air-filled side holes improves the sensitivity of the
sensor.
In another preferred embodiment, two side holes are filled with fluid from
a first supply of fluid, and two side holes are filled with fluid from a
second supply of fluid. The sensor is then used to determine the
differential pressure between the fluid from the first supply of fluid and
the fluid from the second supply of fluid.
Advantageously, the sensor arrangement is very flexible, and may be used to
measure other parameters instead of fluid pressure. For example, one or
more side holes may be filled with a magneto-strictive material so that
the parameter sensed by the sensor is the intensity of a magnetic field.
As another example, one or more side holes may be filled with an
electro-strictive material so that the parameter sensed by the sensor is
the intensity of an electric field. As yet another example, one or more
side holes may be filled with a material with a high thermal expansion
coefficient so that the parameter sensed by the sensor is the temperature
of the material. As yet another example, one or more side holes is filled
with a material that deforms under the influence of a specific chemical
substance so that the parameter sensed by the sensor is the presence of
the specific chemical substance. In another preferred embodiment, one or
more side holes is filled with a temperature compensating material that
compensates for temperature fluctuations in the material that is in one or
more of the remaining side holes.
In accordance with another aspect of the invention, the present invention
provides a method of detecting a difference in frequency between first and
second narrow-banded positive spectral components of an optical signal.
According to the method, at least one of the first and second spectral
components of the optical signal is modulated by a narrow-banded positive
modulation spectral component of a modulation signal. The first and second
spectral components of the optical signal are respectively centered about
first and second frequencies. Similarly, the modulation spectral component
of the modulation optical signal is centered about a modulation frequency.
The modulation produces interference that has an interference frequency
which is a function of the first and second frequencies and the modulation
frequency. The modulation frequency is then varied, causing the
interference frequency to vary. The variation of the interference
frequency is then monitored and, based on this step, the difference in
frequency between first and second spectral components is determined. In a
preferred embodiment, the monitoring step comprises the step of searching
for a value of the modulation frequency that minimizes the interference
frequency.
Advantageously, the detection method according to the present invention may
be implemented using entirely solid state optics/electronics. An
interferometer implemented using free space optics is not required. This
permits a detection system according to the present invention to be
constructed less expensively, more compactly, and in a manner that is more
resistant to vibration as compared to existing detection systems.
Moreover, these benefits are achieved without any loss in precision as
compared to existing detection systems.
Other objects, features, and advantages of the present invention will
become apparent to those skilled in the art from the following detailed
description and accompanying drawings. It should be understood, however,
that the detailed description and specific examples, while indicating
preferred embodiments of the present invention, are given by way of
illustration and not limitation. Many modifications and changes within the
scope of the present invention may be made without departing from the
spirit thereof, and the invention includes all such modifications.
BRIEF DESCRIPTION OF THE DRAWINGS
A preferred exemplary embodiment of the invention is illustrated in the
accompanying drawings in which like reference numerals represent like
parts throughout, and in which:
FIG. 1 is a schematic diagram of a birefringent sensor system according to
one embodiment of the present invention;
FIG. 2A is a perspective view of a preferred birefringent sensor for use in
conjunction with the birefringent sensor system of FIG. 1, and
FIG. 2B is a cross sectional view taken along the lines 2B--2B in FIG. 2A;
FIG. 3A is a perspective view of an arrangement that uses the birefringent
sensor of FIGS. 2A-2B as a pressure sensor,
FIG. 3B is a cross sectional view taken along the lines 3B--3B in FIG. 3A,
and
FIG. 3C is a cross sectional view taken along the lines 3C--3C in FIG. 3B;
FIG. 4 is a view corresponding to FIG. 3C for an alternative arrangement
that uses the birefringent sensor of FIGS. 2A-2B as a differential
pressure sensor;
FIG. 5 is a block diagram of a preferred detection circuit for use in
conjunction with the birefringent sensor system of FIG. 1;
FIG. 6 is a flow chart describing the operation of the detection circuit of
FIG. 5;
FIGS. 7A-7D are graphs of signals at various locations in the detection
circuit of FIG. 5;
FIG. 8 is a block diagram of an alternative detection circuit usable in
conjunction with the birefringent sensor system of FIG. 1; and
FIG. 9 is a frequency domain graph showing the components of interference
produced in the detection system of FIG. 8.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
1. System Overview
Referring now to FIG. 1, a schematic diagram of a birefringent sensor
system 10 is illustrated. By way of overview, the system 10 comprises an
illumination source 12, a network of sensors 15a-15n disposed along an
optical fiber 16, a multiplexer 18, a detection circuit 20, and a signal
processing unit 22. The signal processing unit 22 could be, for example, a
digital signal processor, an analog signal processor, a computer, or any
other suitable signal processing unit. The sensors 15a-15n are optically
coupled to the illumination source 12 by way of a non-dispersive coupler
24 and an optical fiber 26a. The sensors 15a-15n are optically coupled to
the detection circuit 20 by way of the non-dispersive coupler 24 and an
optical fiber 26b. The system 10 is referred to as a multi-point sensing
system because it comprises the multiple sensors 15a-15n that are all
disposed at different locations along the common optical fiber 16.
In operation, the illumination source 12 emits light that is transmitted
though the optical fiber 26a, through the non-dispersive coupler 24, and
to the optical fiber 16. Each sensor reflects only a small portion of the
light that it receives and transmits the rest to the remaining sensors
further down the optical fiber 16. The system 10 is preferably a
wavelength-division multiplexed system, such that the sensors 15a-15n are
all tuned to different wavelengths (i.e., the grating constant .LAMBDA. is
different for each of the sensors 15a-15n). Therefore, the different
sensors 15a-15n reflect different wavelengths depending on the grating
constant .LAMBDA. for the particular sensor. The sensors 15a-15n could be
used to measure any one of a variety of different parameters, such as
fluid pressure, electric field intensity, magnetic field intensity,
temperature, and so on. The construction of various preferred embodiments
of the sensors 15a-15n is described in greater detail below in conjunction
with FIGS. 2A-2B, 3A-3C and 4.
The light reflected from the sensors 15a-15n is reflected back through the
optical fiber 16 to the non-dispersive coupler 24. The coupler 24
transmits half of the light through the optical fiber 26a (this half of
the light being lost), and the other half of the light through the optical
fiber 26b to the multiplexer 18. In the preferred embodiment, the
multiplexer 18 comprises a wavelength division multiplexer (not
illustrated) in series with a time division multiplexer (not illustrated).
The wavelength division multiplexer is coupled to the optical fiber 26b
and associates each pair of reflections with a particular sensor on the
basis of the wavelength of the reflection and stored information
pertaining to the tuned wavelength of the sensors 15a-15n. The wavelength
division multiplexer has a plurality of outputs that each correspond to a
respective one of the sensors 15a-15n and that are connected to inputs of
the time division multiplexer. The time division multiplexer sequentially
selects the outputs of the wavelength division multiplexer. The output of
the time division multiplexer is connected to the detection circuit 20.
This arrangement allows the sensors 15a-15n to be disposed along a common
optical fiber while at the same time permitting the optical signals from
the sensors 15a-15n to be processed sequentially, so that only a single
detection circuit 20 is required.
After receiving the output signal of a selected one of the sensors 15a-15n,
the detection circuit 20 determines the spectral separation between the
two reflections from the selected sensor in order to permit the signal
processing unit 22 to determine the value of the sensed parameter (e.g.,
the amount of a pressure sensed by the selected sensor). The construction
and operation of the preferred embodiment of the detection circuit 20 is
described in greater detail below in conjunction with FIGS. 5, 6 and
7A-7D. Additionally, an alternative embodiment of the detection circuit 20
is described in conjunction with FIGS. 8 and 9.
2. Detailed Description of Preferred Sensor Arrangements
Referring now to FIGS. 2A-2B, a sensor 15 is illustrated in greater detail.
The sensor 15 is intended to generically represent each of the sensors
15a-15n. Accordingly, the description below pertains to all of the sensors
15a-15n.
The optical fiber 16 is a birefringent optical fiber and comprises a core
32 and a cladding 34. The core 32 has a fiber grating 36 recorded therein.
(The longitudinal dimensions of refractive index regions 38 and 40 have
been greatly exaggerated in FIG. 2A as compared to the thickness of the
optical fiber 16 to show the fiber grating 36.) The fiber grating 36 is
reflective at two wavelengths defined by the grating constant .LAMBDA. and
the effective index of refraction (including birefringent effects) as
previously described in conjunction with Eq. (1), and is otherwise
generally transmissive. The fact that the optical fiber 16 is birefringent
maintains separation between the two reflections and prevents coupling
between light from the two polarization modes.
The cladding 34 has a plurality of side holes 31a-31d formed therein. In
practice, the side holes 31a-31d are formed in only a section 16' of the
optical fiber 16 that is used to form the sensor 15. The side holes
31a-31d are drilled into the preform of the section 16' of the optical
fiber 16 during manufacturing, before the section 16- of the optical fiber
16 is drawn down to its final thickness. The section 16' is then fusion
spliced to the remainder of the optical fiber 16. In the preferred
embodiment, four side holes are utilized. However, more or fewer side
holes could also be utilized.
The side holes 31a-31d are substantially coextensively located with respect
to each other along the length of the optical fiber 16. Additionally, the
side holes 31a-31d extend substantially parallel to the core 32 and are
preferably orthogonally positioned with respect to each other and with
respect to the core 32. In other words, when the side holes 31a-31d and
the core 32 are viewed in transverse cross section (FIG. 2B), a first line
42a that extends from the side hole 31a, through the core 32 to the side
hole 31c is preferably substantially perpendicular to a second line 42b
that extends from the side hole 31b through the core 32 to the side hole
31d. (The lines 42a and 42b are shown merely for purposes of illustration
and do not form part of the optical fiber 16.) In general, the side holes
31a-31d could also be arranged such that the lines 42a and 42b are
non-parallel and non-coincident without necessarily being substantially
perpendicular, although the resultant sensor may not work as well.
The sensor 15 may be used to measure a variety of different parameters. For
example, the sensor 15 may be used to measure (1) temperature (by placing
a material with high thermal expansion properties in one or more of the
side holes 31a-31d), (2) fluid pressure (by placing the fluid itself in
one or more of the side holes 31a-31d), (3) electric field intensity (by
placing an electro-strictive material, for example a piezo-electric
material, which deforms under the influence of an electric field in one or
more of the side holes 31a-31d), (4) magnetic field intensity (by placing
a magneto-strictive material that deforms under the influence of a
magnetic field in one or more of the side holes 31a-31d), or (5) the
concentration of a specific chemical substance (by placing a material that
deforms under the concentration of the specific chemical substance in one
or more of the side holes 31a-31d). Other parameters could also be
measured. Two specific examples of the construction and operation of the
sensor 15 are now given in conjunction with FIGS. 3A, 3B, 3C and 4, in
which the sensor 15 is used as a pressure sensor.
Specifically, in FIGS. 3A-3C , the sensor 15 measures the pressure of a
fluid with reference to, for example, a sealed volume of air. As shown in
FIG. 3A, the arrangement comprises the sensor 15 and first and second
disks 44a and 44b that are used to mount the sensor 15 within a pipe 46.
The sensor 15, which is contained in the optical fiber 16, is disposed
between the first and second disks 44a and 44b. The disks 44a and 44b
divide the pipe into first and second regions 47a and 47b. The pipe 46
allows the sensor 15 to be mounted in conventional manner using threads 48
so as to provide the sensor 15 access to a fluid. The fluid, which may be
a liquid or a gas, enters the pipe 46 through an opening 49 at one end of
the pipe.
FIG. 3B illustrates a cross section view taken along the lines 3B--3B in
FIG. 3A, and FIG. 3C illustrates a cross section view taken along the
lines 3C--3C in FIG. 3B. As shown, the first disk 44a has first and second
channels 50a and 50b, respectively, formed therein. The channels 50a and
50b are disposed between an exterior surface of the first disk 44a and an
exterior surface of the optical fiber 16. The channels 50a and 50b are
aligned with first and second access holes 52a and 52b that are formed in
the cladding 34 of the fiber. The first and second access holes 52a and
52b extend from the exterior surface of the optical fiber 16 to the side
hole 31a. The access holes 52a and 52b cooperate with the side hole 31a to
provide a fluid channel in the cladding 34 through which fluid having a
pressure can flow. Although it would be possible to use only a single
access hole, the use of two access holes 52a and 52b is preferred because
it prevents air from becoming trapped in the side hole 31a.
In similar fashion to the first disk 44a, the second disk 44b also has
first and second channels 54a and 54b, respectively, formed therein. The
channels 54a and 54b are disposed between an exterior surface of the
second disk 44b and an exterior surface of the optical fiber 16. The
channels 54a and 54b are aligned with first and second access holes 56a
and 56b that are formed in the cladding 34 of the fiber. The first and
second access holes 56a and 56b extend from the exterior surface of the
optical fiber 16 to the side hole 31c. The access holes 56a and 56b
cooperate with the side hole 31c to provide a fluid channel in the
cladding 34 through which fluid having a pressure can low.
As shown most clearly in FIG. 3C, the side holes 31b and 31d are sealed and
are not coupled to the exterior of the optical fiber 16. The side holes
31b and 31d preferably contain air or some other gaseous substance that is
relatively compressible.
In operation, a supply of fluid fills the region 47a of the pipe 46 by way
of the opening 49. The supply of fluid also fills the region 47b of the
pipe 46 that is disposed on the opposite side of the disks 44a and 44b
relative to the opening 49. For this purpose, the disks 44a and 44b are
provided with a channel 58 that extends through both of the disks 44a and
44b. A similar second channel (not illustrated) that extends through both
of the disks 44a and 44b is also provided so as to prevent air from
becoming trapped on the opposite side of the disks 44a and 44b. The supply
of fluid in the region 47a fills the side hole 31a by way of the channels
50a-50b and the access holes 52a-52b. The supply of fluid in the region
47b fills the side hole 31b by way of the channels 54a-54b and the access
holes 56a-56b.
The fluid exerts a pressure on the walls of the side holes 31a and 31c.
This pressure is directed radially outwardly from the longitudinal
centerline of the side holes 31a and 31c. A portion of the pressure that
is directed radially outwardly from the longitudinal centerline of the
side holes 31a and 31c is also directed radially inwardly toward the
longitudinal centerline of the core 32. This portion of the pressure
places a stress on the core and therefore contributes to stress-induced
birefringence (even absent any physical deformation). As a result, the
birefringence of the optical fiber 16 increases and the spectral
separation of the two reflections produced by the fiber grating 36
increases. Moreover, because the side holes 31b and 31d are filled with
air or another preferably gaseous material, there is less cladding for the
pressure to act upon and a relatively larger portion of the pressure acts
on the core. As a result, the extent to which the birefringence increases
for a given pressure increase is larger than in an optical fiber without
air-filled side holes.
Additionally, another portion of the pressure that is directed radially
outwardly from the longitudinal centerline of the side holes 31a and 31c
is also directed radially outwardly from the longitudinal centerline of
the core 32. This pressure tends to elongate the cross section of the
optical fiber 16 in the direction of the line 42a, such that the optical
fiber becomes slightly elliptical rather than circular. To the extent that
the geometrical asymmetry of the optical fiber 16 increases, the
birefringence of the optical fiber 16 increases and the spectral
separation of the two reflections produced by the fiber grating 36
increases. Moreover, because the side holes 31b and 31d are filled with
air or another preferably gaseous material, it is relatively easier for
the optical fiber 16 to deform and acquire an elliptical shape. As a
result, for this additional reason, the extent to which the birefringence
increases for a given pressure increase is larger than in an optical fiber
without air-filled side holes.
The birefringence of the optical fiber 16 may then be monitored in
conventional fashion to determine the pressure of the fluid in the side
holes 31a and 31c. When there is no additional birefringence (beyond the
inherent birefringence that always biases the optical fiber 16 even absent
any pressure), the pressure of the fluid in the side holes 31a and 31c is
the same as the pressure of the air in the side holes 31b and 31d. Thus,
in the arrangement of FIGS. 3A-3C, the sensor 15 measures the pressure of
a fluid with reference to the pressure of a sealed volume of air.
It should be noted that the sensor 15 could be constructed and arranged
such that an increase in pressure would tend to decrease (rather than
increase) birefringence. In this instance, it may be necessary to utilize
a polarization sensitive detection scheme in order to ensure that the two
reflections (which each correspond to a different polarization mode) can
be adequately distinguished.
It should also be noted that the sensor 15 could be constructed using only
two side holes, one of which contains fluid and the other of which
contains another material such as air. More than four side holes could
also be used.
Finally, it should be noted that instead of filling the side holes 31b and
31d with air, the side holes 31b and 31d could be filled with a
temperature compensating material. For example, the side holes 31b and 31d
could be filled with the same type of fluid that fills the side holes 31a
and 31c. In this instance, as the pressure of the fluid in the side holes
31a and 31c increases due only to an increase in temperature, the pressure
of the fluid in the side holes 31b and 31d also increases by a
corresponding amount. The pressure in the side holes 31b and 31d acts
orthogonally to, and tends to offset, the pressure in the side holes 31a
and 31c. The fluid in the side holes 31b and 31d is thus able to achieve
temperature compensation for the fluid in the side holes 31a and 31c.
Referring now to FIG. 4, a second preferred arrangement that uses the
sensor 15 is illustrated. In the second arrangement, the side holes 31b
and 31d are filled with a second fluid, and the sensor 15 measures the
differential pressure between the fluid in the side holes 31a and 31c and
the fluid in the side holes 31b and 31d.
As shown, the arrangement of FIG. 4 comprises an additional third disk 44c.
The third disk 44c isolates the region 47a from the region 47b.
Additionally, a channel 60 is formed between the disks 44b and 44c that
couples the channel 54a to the channel 58. A similar arrangement is
provided for the channel 54b. As a result, the side holes 31a and 31c are
filled using only the supply of fluid in the region 47a, and not the
supply of fluid in the region 47b.
The side holes 31b and 31d are coupled to the supply of fluid in the region
47b. A second opening (not illustrated) may be formed in the pipe 46 at an
opposite end of the pipe as the opening 49 in order to allow the second
supply of fluid to fill the region 47b. The side holes 31b and 31d are
coupled to the second supply of fluid by way of channels 62, 64 and 66,68
respectively. Additional access holes 70 and 72 are formed in the cladding
that extend from the side holes 31b and 31d to the channels 64 and 68,
respectively, at the exterior surface of the optical fiber 16. As in the
case of the side holes 31a and 31c (see Fib. 3B), this channel arrangement
is provided at both longitudinal ends of the side holes 31b and 31d.
In operation, fluid fills the side holes 31a-31d. The fluid that fills the
side hole 31a and the fluid that fills the side hole 31c are from the
common supply of fluid in the region 47a. The fluid that fills the side
hole 31b and the fluid that fills the side hole 31d are from the common
supply of fluid in the region 47b. The fluid in the holes 31a-31d exerts
pressure on the walls of the side holes 31a-31d that is directed radially
outwardly from the center of each the holes 31a-31d.
Pressure from fluid in the holes 31a and 31c is directed along the line 42a
inwardly toward the core as well as outwardly toward the exterior of the
optical fiber 16. Pressure from fluid in the holes 31b and 31d is directed
along the line 42b inwardly toward the core as well as outwardly toward
the exterior of the optical fiber 16. Thus, the pressure from the fluid in
the side holes 31b and 31d acts orthogonally to (and tends to offset) the
pressure from the fluid in the side holes 31a and 31c. Consequently, the
optical fiber 16 becomes more or less birefringent depending on which
pressure is larger. Accordingly, the sensor 15 measures the differential
pressure between the fluid in the side holes 31a and 31c and the fluid in
the side holes 31b and 31d.
Again it should be noted that, while in the preferred embodiment four side
holes are used, other numbers of side holes could also be used. For
example, only two side holes could be used, one of which is filled with
fluid from a first supply of fluid and the other of which is filled with
fluid from a second supply of fluid. Alternatively, four side holes could
be used, two of which measure differential pressure and the other two of
which perform temperature compensation as previously described.
Additionally, more than four side holes could also be used.
A number of advantages of the particular preferred embodiment of the sensor
should therefore be recognized. First, the sensor exhibits increased
sensitivity due to the provision of side holes that are filled with a
compressible, deformable material such as air. A smaller amount of
pressure or other measured parameter can induce a larger birefringence
because the optical fiber is more sensitive to stress (since there is less
material for the stress to act upon) and because the optical fiber is more
deformable (since there is less material that resists deformation).
Additionally, the sensor is very flexible and can be used in a variety of
different applications. The sensor can be used as a pseudo-absolute
pressure sensor in which the pressure of a fluid is referenced, for
example, against the pressure of a sealed volume of air. The sensor can
also be used as a differential pressure sensor in which the difference in
pressure between two different fluids is measured. The sensor can also be
constructed and arranged so as to have built-in temperature compensation.
Finally, the sensor can measure a variety of other parameters besides
pressure by placing different materials in the side holes, such as
magneto-strictive materials, electro-strictive materials, and thermally
expansive materials.
3. Detailed Description of Preferred Detection Circuit
Referring now to FIGS. 5, 6, and 7A-7D, the detection circuit 20 is
described in greater detail. FIG. 5 is a block diagram of the detection
circuit 20, FIG. 6 is a flow chart describing the operation of the
detection circuit 20, and FIGS. 7A-7D are graphs of signals at various
locations in the detection circuit 20.
The purpose of the detection circuit 20 is to determine the difference in
wavelength or optical frequency between the two reflections received from
the sensor 15. (It is well known that a wavelength .lambda. is related to
a corresponding optical frequency .omega. by the relationship
##EQU1##
where c.sub.0 is the speed of light in a vacuum. In describing the
operation of the detection circuit 20, frequency is used instead of
wavelength to describe the spectral properties of the signal from the
sensor 15.) The frequencies of the two reflections from the sensor 15 are
too high for a photodetector to measure the frequencies and determine
their difference directly. Therefore, the detection circuit 20 provides a
way to determine the frequency difference indirectly.
By way of overview, the operation of the detection circuit is preferably as
follows: A technique is used in which the optical signal from the sensor
15 is amplitude modulated with a high frequency electrical modulation
signal. The modulation creates additional spectral components (commonly
referred to as side bands) in the optical signal. The interference
produced using the additional spectral components, which is of a lower
frequency, can be monitored using a photodetector. The modulation
frequency can be varied in a controlled way in order to minimize the
frequency of the interference signal observed at the photodetector. When
the frequency of the interference signal is at a minimum, a known
relationship exists between the frequency of the modulation signal and the
difference in frequency between the two reflections. Therefore, the
frequency of the modulation signal can be used to determine the difference
in frequency between the two reflections.
s.sub.1
(t)=A.sub.1.multidot.cos(.omega..sub.1.multidot.t)+A.sub.
2.multidot.cos(.omega.hd 2.multidot.t) (2)
where t is time, A.sub.1 is the amplitude of the first reflection,
.omega..sub.1 is the optical frequency of the first reflection, A.sub.2 is
the amplitude of the second reflection, and .omega..sub.2 is the optical
frequency of the second reflection. The Fourier transform of the signal
s.sub.1 (t) is as follows:
s.sub.1
(.omega.)=A.sub.1.multidot..pi.[.delta.(.omega.-.omega..sub.
1)+.delta.(.omega.+.omega..sub.1)]+A.sub.
2.multidot..pi.[.delta.(.omega.-.omega..sub.2)+.delta.(.omega.+.omega..
sub.2)] (3)
FIG. 7A illustrates the corresponding frequency domain representation of
the signal s.sub.1 (t). As previously noted, the reflections in practice
comprise a plurality of narrow-banded spectral components 92a, 92b, 94a
and 94b. The spectral components 92a and 92b correspond to one of the
reflections and the spectral components 94a and 94b correspond to the
other of the reflections. The spectral components 92a and 94a are the
positive spectral components and are centered about positive optical
frequencies .omega..sub.1 and .omega..sub.2, respectively. The spectral
components 92b and 94b are negative spectral components and correspond to
the spectral components 92a and 94a, respectively. The spectral components
92b and 94b are centered about negative optical frequencies -.omega..sub.1
and -.omega..sub.2, respectively. For clarity purposes, the spectral
components 92a-b and 94a-b are modeled in Eqs. (2) and (3) using the dirac
delta function (.delta.) as occurring at discrete optical frequencies
.omega..sub.1, -.omega..sub.1, .omega..sub.2 and -.omega..sub.2,
respectively.
At step 104, the optical modulator 82 multiplies the signal s.sub.1 (t)
with a modulation signal m(t), thereby producing the amplitude modulated
signal s.sub.2 (t). The modulation signal m(t) is a high frequency
electrical signal. (Of course, the signal m(t) is nevertheless of a lower
frequency than the optical signal s.sub.1 (t), since electrical signals
are always of lower frequency than optical signals.) As described further
below, the frequency of the signal m(t) is varied in order to determine
the frequency at which the minimum interference frequency occurs. For
present purposes, however, it is assumed temporarily that the frequency of
the signal m(t) is not varied. In this case, the signal m(t) has the
following form:
m(t)=A.sub.3.multidot.cos(.omega..sub.3.multidot.t) (4)
where A.sub.3 is the amplitude of the signal m(t) and .omega..sub.3 is the
frequency of the signal m(t). The Fourier transform of the signal m(t) is
as follows:
m(.omega.)=A.sub.3.multidot..pi.[.delta.(.omega.-.omega..sub.
3)+.delta.(.omega.+.omega..sub.3)] (5)
The corresponding frequency domain representation of the signal m(t) is
shown in FIG. 7B.
The amplitude modulation (i.e., multiplication) of the signal m(t) with the
signal s.sub.1 (t) produces a signal s.sub.2 (t). The signal s.sub.2 (t)
has the following form:
s.sub.2 (t)=(A.sub.1.multidot.cos(.omega.hd
1.multidot.t)+A.sub.2.multidot.cos(.omega..sub.2.multidot.t)).multidot.(A.
sub.3.multidot.cos(.omega..sub.3.multidot.t)) (6)
The Fourier transform of the signal s.sub.2 (t) is as follows:
##EQU2##
For purposes of simplification, Eq. (7) can be rewritten as follows:
##EQU3##
where the terms D.sub.1 -D.sub.8 replace the dirac delta functions of Eq.
(7). The corresponding frequency domain representation of the signal
s.sub.2 (t) is shown in FIG. 7C.
At step 106, the signal s.sub.2 (t) is detected at the photodetector 86.
When the D.sub.2 and D.sub.5 components (and therefore the D.sub.4 and
D.sub.7 components) are sufficiently close together, observable
interference occurs. The interference has the following form:
I(t)=[B.sub.1 cos[(.omega..sub.1 +.omega..sub.3)t+.theta..sub.1 ]+B.sub.2
cos[(.omega..sub.2 -.omega..sub.3)t+.theta..sub.2 ]].sup.2 (9)
where .theta..sub.1 and .theta..sub.2 are the starting phases and B.sub.1
and B.sub.2 are constants. The constants B.sub.1 and B.sub.2 are both
functions of the constants A.sub.1, A.sub.2 and A.sub.3 (where B.sub.1
=1/2A.sub.1 A.sub.3, B.sub.2 =1/2A.sub.2 A.sub.3). (The particular value
of the constants A.sub.1, A.sub.2 and A.sub.3 does not matter so long as
the interference is of sufficient magnitude to be measurable.) Equation
(9) does not incorporate the terms D.sub.1, D.sub.3, D.sub.5 and D.sub.8
since these terms do not produce observable interference. Equation (9) can
be rewritten as follows:
##EQU4##
The output of the photodetector 86 cannot respond to the components at the
frequencies 2(.omega..sub.2 -.omega..sub.3), 2(.omega..sub.1
+.omega..sub.3), ((.omega..sub.2 -.omega..sub.3)+(.omega..sub.1
+.omega..sub.3)). Therefore, only the first and fourth terms of Eq.(10)
are observable by the photodetector 86, and the interference that is
observed has the following form:
I(t)=1/2(B.sub.1.sup.2 +B.sub.2.sup.2)+B.sub.1 B.sub.2 cos[((.omega..sub.2
-.omega..sub.3)-(.omega..sub.1 +.omega..sub.3))t+(.theta..sub.2
-.theta..sub.1)] (11)
Equation (11) may be simplified by reorganizing the frequency terms and by
again replacing the constants B.sub.1 and B.sub.2 with new constants
C.sub.1 and C.sub.2 (where C.sub.1 =1/2(B.sub.1.sup.2 +B.sub.2.sup.2),
C.sub.2 =B.sub.1.multidot.B.sub.2).
I(t)=C.sub.1 +C.sub.2 cos[((.omega..sub.2
-.omega..sub.1)-2.omega..sub.3)t+(.theta..sub.2 -.theta..sub.1)] (12)
The C.sub.1 term is a DC term that is independent of the frequency
.omega..sub.3. The C.sub.2 cos[((.omega..sub.2
-.omega..sub.1)-2.omega..sub.3)t+(.theta..sub.2 -.theta..sub.1)]term has a
frequency that varies according to the term ((.omega..sub.2
-.omega..sub.1)-2.omega..sub.3). The frequency of this term is therefore
equal to zero when the term ((.omega..sub.2
-.omega..sub.1)-2.omega..sub.3) is equal to zero, that is, when the
following condition is met:
##EQU5##
Based on Eq. (13), the difference between the frequencies .omega..sub.1 and
.omega..sub.2 may be determined in steps 108-116 in the following manner.
In step 108, the frequency of the interference observed by the
photodetector 86 is determined. At step 110, it is determined whether the
observed frequency is a minimum interference frequency. Since the
frequency of the modulation signal m(t) is continuously varied in the
manner shown in FIG. 7D (step 112), the frequency of the interference
signal experiences a periodic minimum value. Thus, at step 110, the output
of the photodetector 86 is continuously monitored as the frequency
.omega..sub.3 is varied in order to identify the instant at which the
frequency of the interference is minimized. The monitoring may be
performed by the signal processing unit 22, which is coupled to the
photodetector 86 by way of an amplifier 88 and a frequency to voltage
converter 90.
At step 114, the value of the modulation frequency .omega..sub.3 that
causes the minimum frequency of the interference is determined. The
relationship between (1) the modulation frequency .omega..sub.3 and (2)
the difference between the optical frequencies .omega..sub.1 and
.omega..sub.2 is known and is given by Eq. (13). Therefore, at step 116,
the difference between the optical frequencies .omega..sub.1 and
.omega..sub.2 may be determined by determining the modulation frequency
.omega..sub.3 at which the frequency of the interference is minimized and
applying Eq. (13).
It may be noted that Eq. (13) assumes that the interference frequency is
equal to zero whereas in step 110 a search is performed for the minimum
frequency. Conceivably, the search could determine a value of the
modulation frequency .omega..sub.3 at which the frequency of the
interference is equal to zero. In practice, however, it ordinarily will
not be possible to determine the precise frequency that causes the
interference frequency to be equal to zero, especially since the signal
s.sub.1 (t) produced by the sensor 15 may not have a completely constant
frequency. Therefore, the difference between the optical frequencies
.omega..sub.1 and .omega..sub.2 is determined on the basis of the
modulation frequency .omega..sub.3 at which the frequency of the
interference is at a minimum, as opposed to the modulation frequency
.omega..sub.3 at which the frequency of the interference is equal to zero.
To the extent that the frequency of the interference is non-zero, this
simply represents a slight error in the measurement.
It should also be noted that, although the detection circuit 20 is
preferably used in conjunction with the sensor 15 described above, the
detection circuit could also be used with other types of devices. For
example, the detection circuit 20 in conjunction with birefringent grating
sensors could also be used for performing multi-axial strain measurements.
In general, the detection circuit 20 could be used in conjunction with any
sensor or other device in which a signal is produced at two frequencies
and in which it is desired to determine the difference between the two
frequencies, regardless of the physical construction of the device.
It should also be noted that the two positive (and two negative) spectral
components are in orthogonal polarization states, and therefore are easily
separable using, for example, a polarization-dependent beam splitter or a
polarization splitting coupler which may be placed at the input of the
detection circuit 20. This allows the optical fiber that carries the
signal from the sensor 15 to be split into two optical paths, each of
which carries one of the two spectral components. Further, this allows the
two spectral components to be manipulated independently, for example, by
multiplying them by different modulation signals having different
modulation frequencies. However, this also requires that the polarization
states of the two spectral components be matched. This could be
accomplished, for example, using a half-wave plate (when using a
polarization-dependent beam splitter) or by properly orienting the two
optical fibers about the polarization axis (when using the polarization
splitting coupler).
It should also be noted that while in the preferred embodiment heterodyne
detection is used (in which the optical signal s.sub.1 (t) is mixed with
another signal m(t)), homodyne detection could also be used. In this case,
the optical signal s.sub.1 (t) is mixed with itself in order to produce a
lower frequency component. The lower frequency component of the signal
s.sub.1 (t) may then be caused to interfere a variable frequency
modulation signal m(t) as previously described.
Referring now to FIGS. 8-9, an alternative embodiment of the detection
circuit 20 is illustrated. FIG. 8 corresponds to FIG. 5 and indicates the
differences between the detection circuit 20 and a modified detection
circuit 20'. In the detection circuit 20' a summing junction 92 is
disposed between a modulator 82' and the photodetector 86. Instead of
being an amplitude modulator as in FIG. 1, the modulator 82' could instead
be a phase modulator. Additionally, a frequency modulator or polarization
modulator could also be used. For purposes of describing the invention, it
is now assumed that the modulator 82' is an amplitude modulator.
The summing junction 92 receives the optical signal s.sub.1 (t) directly
from the multiplexer 18. Of course, the output s.sub.3 (t) of the summing
junction 92 is the summation of the optical signals s.sub.1 (t) and
s.sub.2 (t). The Fourier transforms of the optical signals s.sub.1 (t) and
s.sub.2 (t) are given in Eqs. (3) and (7), respectively.
FIG. 9 corresponds to FIG. 7C and shows a frequency domain representation
of the signals s.sub.1 (t) and s.sub.2 (t) which are both detected by the
photodetector 86. (For simplicity, only the positive spectral components
of the signals s.sub.1 (t) and s.sub.2 (t) are shown in FIG. 9.) As
apparent from FIG. 9, observable interference between the signals s.sub.1
(t) and s.sub.2 (t) occurs (1) between the .omega..sub.1 component of the
signal s.sub.1 (t) and the .omega..sub.2 -.omega..sub.3 component of the
signal s.sub.2 (t), and (2) between the .omega..sub.2 component of the
signal s.sub.1 (t) and the .omega..sub.1 +.omega..sub.3 component of the
signal s.sub.2 (t). The frequency of the interference will be the same in
both instances and will be equal to zero when .omega..sub.1 =.omega..sub.2
-.omega..sub.3 and .omega..sub.2 =.omega..sub.1 +.omega..sub.3 or,
alternatively stated, when the following condition is met:
.omega..sub.3 =.omega..sub.2 -.omega..sub.1 (14)
Therefore, the difference in optical frequencies between the optical
signals s.sub.1 (t) and s.sub.2 (t) may be determined by performing the
process described in FIG. 6 in conjunction with Eq. (14).
It should be noted that the system of FIG. 5 is preferred over the system
of FIG. 8 because the frequency .omega..sub.3 of the high frequency
electrical modulation signal m(t) need only be half as high in the system
of FIG. 5 in order to minimize the interference frequency. This is
apparent from a comparison of Eqs. (13) and (14). In practice, it is
significantly easier to generate a frequency .omega..sub.3 that satisfies
the condition of Eq. (13) as compared to a frequency .omega..sub.3 that
satisfies the condition of Eq. (14).
Advantageously, the detection system according to the present invention may
be constructed using entirely solid state optics/electronics, an
interferometer implemented using free space optics is not required. This
permits the detection system to be constructed less expensively, more
compactly, and in a manner that is more resistant to vibration as compared
to existing detection systems. These benefits are achieved without any
loss in precision as compared to existing detection systems.
Many other changes and modifications may be made to the present invention
without departing from the spirit thereof. The scope of these and other
changes will become apparent from the appended claims.
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